Divisor

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For the second operand of a division, see division (mathematics).

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder.

[change] Explanation

For example, 7 is a divisor of 42 because 42/7 = 6. We also say 42 is divisible by 7 or 42 is a multiple of 7 or 7 divides 42 or 7 is a factor of 42 and we usually write 7 | 42. For example, the positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

In general, we say m|n (read: m divides n) for non-zero integers m and n iff there exists an integer k such that n = km. Thus, divisors can be negative as well as positive, although often we restrict our attention to positive divisors. (For example, there are six divisors of four, 1, 2, 4, -1, -2, -4, but one would usually mention only the positive ones, 1, 2, and 4.)

1 and −1 divide (are divisors of) every integer, every integer is a divisor of itself, and every integer is a divisor of 0, except by convention 0 itself (see also division by zero). Numbers divisible by 2 are called even and numbers not divisible by 2 are called odd.

A divisor of n that is not 1, −1, n or −n is known as a non-trivial divisor; numbers with non-trivial divisors are known as composite numbers, while prime numbers have no non-trivial divisors.

The name comes from the arithmetic operation of division: if a/b = c then a is the dividend, b the divisor, and c the quotient.

There are properties which allow one to recognize certain divisors of a number from the number's digits.

[change] Other websites

• Online Number Factorizer Instantly factors numbers up to 17 digits long
• Factoring Calculator -- Factoring calculator that displays the prime factors and the prime and non-prime divisors of a given number.